In this note, generalized connections σT,f are investigated, where AσT,fB = TAfT − A (B) for positive semidefinite matrix A and hermitian matrix B, and operator monotone function f : J → R on an interval J ⊂ R. Here the symbol T A denotes a reflexive generalized inverse of a positive bounded linear operator TA. The problem of estimating a given generalized connection by other ones is studied. T...

In this paper, we introduce and study a system of mixed variational-like inclusions and a system of proximal operator equations in Banach spaces which contains variational inequalities, variational inclusions, resolvent equations, system of variational inequalities and system of variational inclusions in the literature as special cases. It is established that the system of mixed variational-lik...

Let T, T ′ be weak contractions (in the sense of Sz.-Nagy and Foiaş), m, m the minimal functions of their C0 parts and let d be the greatest common inner divisor of m, m . It is proved that the space I(T, T ) of all operators intertwining T, T ′ is reflexive if and only if the model operator S(d) is reflexive. Here S(d) means the compression of the unilateral shift onto the space H⊖dH. In parti...

and Applied Analysis 3 nonexpansive mapping such that F S ∩ A−10/ ∅. Let {xn} be a sequence generated by x0 x ∈ C and un J−1 ( βnJxn ( 1 − βn ) JSJrnxn ) , Cn { z ∈ C : φ z, un ≤ φ z, xn } , Qn {z ∈ C : 〈xn − z, Jx0 − Jxn〉 ≥ 0}, xn 1 ΠCn∩Qnx0 1.6 for all n ∈ N ∪ {0}, where J is the duality mapping on E, {βn} ⊂ 0, 1 , and {rn} ⊂ a,∞ for some a > 0. If lim infn→∞ 1 − βn > 0, then {xn} converges s...

In this article, the spectral theory is considered, we study families and their correspondence to operators on reflexive Banach spaces; assume A a well-bounded operator Lebesgue spaces then scalar type operator. The main goals are obtain characterization of in terms associated family topology dual pairing construct continuous functional calculus for space.

The aim of this paper is to show that the automorphism and isometry groups of the suspension of B(H), H being a separable infinite dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively local surjective isometry of C0(R) ⊗ B(H) is an automorphism, respectively a surjective isometry.

In the paper, we define a notion of prereflexivity for subspaces, give several equivalent conditions of this notion and prove that if $ C_ L(H) is prereflexive, then every aweakly closed subspace of S is prereflexive if and only if $ has the property WP(see definition 2.11). By our result, we construct a reflexive operator A such that A 0 is not prereflexive.

The aim of this note is to study convergence and convergence rates of the regularized solutions for the operator equation of Hammerstein type x + F2F1(x) = f in reflexive Banach spaces under the non-monotone perturbations F h 2 and F h 1 of the operators F2 and F1, respectively.

We establish variational principles for monotone and maximal bifunctions of Brøndsted-Rockafellar type by using our characterization of bifunction’s maximality in reflexive Banach spaces. As applications, we give an existence result of saddle point for convex-concave function and solve an approximate inclusion governed by a maximal monotone operator.

We construct a Banach space X of Gowers-Maurey type such that the algebra bounded operators L(X) is direct sum an infinite dimensional reflexive and operator ideal strictly singular SS(X).